Ask the Slot Expert: Split Card calculations: Straight Flush - Part 1

Previously on Ask the Slot Expert:

A few weeks ago I played Deuces Wild with the Split Card gimmick. Split Card sometimes gives you two cards in one position of your hand. Although it's possible to get 6 of a Kind and other six-card hands, the only bonus hand is 5 Deuces, which pays 2000.

I was dealt this hand: Q♦ 2♠/2♠ 2♥ T♦ 8♥.

I wasn't sure which combination was better to hold:

1. Q♦ 2♠/2♠ 2♥ T♦ and be guaranteed the Wild Royal and maybe get 4 Deuces
2. 2♠/2♠ 2♥ and take a chance on 5 Deuces

Here is the EV of option 1.

Here is what I have so far for the EV of option 2.

Let's start on Straight Flush. The easiest way to do the calculations is to look at each straight sequence separately. We'll look at combinations we can be dealt with the lowest card in the sequence and find the number of ways we can fill the fifth position without getting a higher-paying hand or double-counting a combo.

We get a little bit of a break. We only have to do sequences beginning with A, 3, 4, 5, 6, 7, 8, and 9.

We'll begin with 34567 because it's straightforward and the same for all four suits. I'll show the calculations in a table.

The Tot Ways column shows the total number of ways to get a Straight Flush in the sequence specified. The Ways column shows the number of ways to get a Straight Flush in the suits specified. In this case, the calculations are the same for all four suits because the ranks in the sequence are complete in the cards remaining in the deck. The Suit(s) column shows the suit or suits for which the details that follow apply.

The Deal columns show the two or three cards we were dealt. The next set of columns shows the number of cards of each rank we have to remove from the cards remaining in the deck to avoid a higher-paying hand or double-counting a combination.

The final column is "Fill", which gives the number of ways to fill the fifth position without getting a higher-paying hand or double-counting. For the two-card combos, the column is 43 minus the number of cards we removed. (Remember why it's 43? There are 47 cards left in the deck, minus two deuces that would give us a higher-paying hand [4 Deuces], minus the two cards dealt.) For the three-card combos, it's 1. There's only one way to rock -- er, to get dealt those three cards.

The first combo in the table is 34. We don't want a suited Ace; we'll deal with an Ace-low Straight Flush in another table. We don't want any of the other 3s or 4s in the deck (3 each) because that would give us 5 of a Kind. We don't want a suited 5, 6, or 7 because we'll deal with getting dealt three suited cards in the sequence later. The sum of the numbers under the rank headings is 10 and 43-10=33.

The combo 35 is similar to 34. The number under rank 4 is 1 because we only have to avoid the suited 4. The number under 5 goes up to 3 because we don't want to get a 5 of a Kind. The total ways to fill is still 33.

For 36 and 37, the second 3 under the ranks moves to the right as per the second card in the combo. In each case the total ways to fill is 33.

The next six entries pick up the ways to be dealt three suited cards in the sequence beginning with a 3. We want to fill out the hand using two cards from 4567. I listed the six combos, but you probably remember that six is the combination of four items taken two at a time.

The last line is the sum of the numbers in the Fill column, 138. The calculations apply to all four suits, so Ways is 4*138=552. The sum of all the numbers in the Ways column is also 552.

There 552 ways to get a 3-low Straight Flush.

Next week we'll tackle sequences in which he have to do diamonds or hearts separately.

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